Which is the equivalent SQL query for the given relational algebra expression

Which is the equivalent SQL query for the given relational algebra expression?

Question:

7. Consider relations(tables) R(A, B, C) and S(B, D). Which of the given SQL queries are equivalent to the Relational Algebra expression "Π_{A, R.B, C, S.B, D}(R X S)"?

(a) SELECT * FROM R, S;
(b) SELECT * FROM R, S WHERE R.B = S.B;
(c) SELECT A, R.B, C, S.B, D FROM R, S;
(d) SELECT A, R.B, C, D FROM R, S WHERE R.B = S.B;

Answer:

Both (a) and (C)

SELECT with * or SELECT with all attributes are equal to the Projection operation in relational algebra. Hence, for the given relational algebra projection on R X S, the equivalent SQL queries are both (a) and (c)

The queries in options (b) and (d) are operations involving a join condition. These two queries are equivalent to a SELECTION operation in relational algebra with a JOIN condition or PROJECTION operation with a JOIN condition.
The query "SELECT * FROM R, S WHERE R.B = S.B;" is equivalent to "σ_{R.B = S.B}(R X S)".
The query "SELECT A, R.B, C, D FROM R, S WHERE R.B = S.B;" is equivalent to "σ_{R.B = S.B}(R X S)".

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